Embedding of classical polar unitals in PG(2,q2)

Gábor Korchmáros, Alessandro Siciliano, T. Szőnyi

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A unital, that is, a block-design 2−(q3+1,q+1,1), is embedded in a projective plane Π of order q2 if its points and blocks are points and lines of Π. A unital embedded in PG(2,q2) is Hermitian if its points and blocks are the absolute points and non-absolute lines of a unitary polarity of PG(2,q2). A classical polar unital is a unital isomorphic, as a block-design, to a Hermitian unital. We prove that there exists only one embedding of the classical polar unital in PG(2,q2), namely the Hermitian unital.

Original languageEnglish
Pages (from-to)67-75
Number of pages9
JournalJournal of Combinatorial Theory. Series A
Volume153
DOIs
Publication statusPublished - Jan 1 2018

Fingerprint

Unital
Block Design
Line
Polarity
Projective plane
Isomorphic

Keywords

  • Embedding
  • Finite Desarguesian plane
  • Hermitian curve
  • Unital

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

Embedding of classical polar unitals in PG(2,q2). / Korchmáros, Gábor; Siciliano, Alessandro; Szőnyi, T.

In: Journal of Combinatorial Theory. Series A, Vol. 153, 01.01.2018, p. 67-75.

Research output: Contribution to journalArticle

Korchmáros, Gábor ; Siciliano, Alessandro ; Szőnyi, T. / Embedding of classical polar unitals in PG(2,q2). In: Journal of Combinatorial Theory. Series A. 2018 ; Vol. 153. pp. 67-75.
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